Method and System for Measuring the Zeta Potential Of the Cylinder&#39;s Outer Surface and the Inside Surface of the Tube

ABSTRACT

The present invention discloses methods and systems for measuring the zeta potential of the cylinder&#39;s outer surface and the inside surface of the tube. In the measuring cell for measuring the zeta potential of the cylinder&#39;s outer surface, the cylinder is placed coaxially inside the reference tube, and the channel existing between the cylinder and the reference tube forms a annular flow channel. Additionally, in the measuring cell for measuring the inside surface of the tube, a reference cylinder is held coaxially inside the tube and a given solution is forced to flow through the annular space between the tube and the reference cylinder.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation in part of applicant's earlier application Ser. No. 11/531,256, filed Sep. 12, 2006.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is generally related to a method and a system for measuring zeta potential, and more particularly to a method and a system for measuring the zeta potential of the cylinder's outer surface and the inside surface of the tube.

2. Description of the Prior Art

Membrane technology was focused on flat membrane during early development while the development of tubular membrane was started around in 1960s from hollow-fiber membrane used in gas separation made by DuPont. Because hollow-fiber membrane has advantages of high specific surface area per unit volume and self-supporting property, it is extensively applied in gas separation, reverse osmosis, hemodialysis, ultrafiltration, microfiltration, and so forth.

Membrane electric charge generally plays an important role in determining its separation performance. Currently, the measurement of zeta potential of membrane focuses on flat membranes. In practice, tubular membrane has been extensively applied in the industry but there is no method provided to measure the zeta potential of the outer surface of tubular membrane. Thus, generally the industry or researchers accept the information supplied by the manufacturer to qualitatively determine the charge property of the membrane. However, membrane electric charges are affected by not only material of the membrane but also the property of solution, such as pH value and ionic intensity. Since there is no effective method provided to quantitatively characterize the charge of the outer surface of cylindrical type objects, therefore it is required to develop a method and measurement system for measuring zeta potential of the cylinder's outer surface, especially the zeta potential of the outer surface of cylindrical membranes. According to the zeta potential, filtration conditions designed to reduce the membrane fouling can be provided and thus the filtration capacity and the selectivity in separation can be enhanced.

On the other hand, it is required to develop a method and measurement system for measuring zeta potential at inside surface of the tube. The electrical potential occurring from the material surface contacted with the solution plays an important role in its industrial application. Currently, most of the measurement of membrane zeta potential focuses on flat membranes. In practice, tubular structure has been extensively applied in the industry but there is no known method of measuring the zeta potential at inside surface of the tubular structure (such as Ceramic tubular structure). Therefore, there is still a need to develop a method and system for measuring zeta potential at inside surface of the tubular structure. The obtained information of zeta potential at inside surface of the tubular structure is very critical for materials preparation, modification, or operating conditions.

SUMMARY OF THE INVENTION

According to the above background, the present invention provides method and system to measure the zeta potential of the cylinder's outer surface and the inside surface of the tube in annular flow to fulfill the requirements of this industry.

The first object of the present invention is to measure the zeta potential of the cylinder's outer surface by annular pipe design. At first, providing a cylinder having a first radius and a reference tube having a second radius, wherein the first radius is smaller than the second radius, and the cylinder is placed coaxially inside the reference tube, and the channel existing between the cylinder and the reference tube forms a annular flow channel. Next, introducing a solution to the annular flow channel, and the solution is forced by a pressure difference ΔP to flow through the annular flow channel. Afterward, performing a measuring process to measure the streaming potential difference between the two ends of the annular flow channel by electrodes, wherein the measuring process comprises calculating the zeta potential ξ_(m) of the cylinder's outer surface from the following equation:

$\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$

where D is the permittivity, ζ_(ref) is the zeta potential of the reference tube, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model.

The second object of the present invention is to provide a system for measuring the zeta potential of the cylinder's outer surface by annular pipe design, comprising a feeding module, a measurement module comprising a reference tube, wherein the measurement module receives a solution from the feeding module, the solution is forced to flow through the inner side of the reference tube, which forms a straight flow channel, and then the solution is discharged to a discharging module so as to form a first measuring course, and thus the measurement module generates a first potential difference signal via the first measuring course, and besides, the cylinder and the reference tube are assembled to form a second measuring course, the radius of the cylinder is smaller than that of the reference tube, the cylinder is coaxial with the reference tube, the solution received by the measurement module is forced to flow through the annular flow channel between the cylinder and the reference tube, and is discharged to the discharging module so as to form the second measuring course, and the measurement module generates a second potential difference signal via the second measuring course, at least one pressure detector for measuring the pressure difference for solution flow from the inlet to the outlet of the flow channel to generate a pressure difference signal, and a calculation module, comprising calculating the zeta potential ξ_(m) of the cylinder's outer surface:

$\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$

where D is the permittivity, ζ_(ref) is the zeta potential of the reference tube, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model, the calculation module receives the first potential difference signal and the pressure difference signal to calculate the zeta potential ξ_(ref) of the inner surface of the reference tube, and the calculation module receives the second potential difference signal and the pressure difference signal accompanying with the zeta potential ξ_(ref) of the inner surface of the reference tube to calculate the zeta potential ξ_(m) of the outer surface of the cylinder.

The third object of the present invention is to provide a method for measuring the zeta potential at inside surface of tubular structure. First, providing a tube having a first radius and a reference cylinder having a second radius, wherein the first radius is greater than the second radius, and the reference cylinder is held coaxially inside the tube, and the channel existing between the tube and the reference cylinder forms an annular flow channel. Next, introducing a solution to the annular flow channel, and the solution is forced by a pressure difference ΔP to flow through the annular flow channel, wherein the flow direction of the solution is parallel to the axial direction of the reference cylinder. Afterward, performing a measuring process to measure the streaming potential difference Ē between the two ends of the annular flow channel by electrodes, wherein the measuring process comprises calculating the zeta potential ξ_(m) at inside surface of the tube from the following equation:

$\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k_{m}}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$

where D is the permittivity, ζ_(ref) is the zeta potential of the reference cylinder, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model.

The fourth object of the present invention is to provide a system for measuring the zeta potential at inside surface of the tube, comprising: a feeding module; a measurement module comprising a reference cylinder and a tube, wherein the reference cylinder is held coaxially inside the tube, and the radius of the tube is greater than the radius of reference cylinder, and the zeta potential of reference cylinder is known or measured in advance, wherein the measurement module receives a solution from the feeding module, the solution is forced to flow through an annular flow channel between the reference cylinder and the tube, and then the solution is discharged to a discharging module so as to form a measuring course, and thus the measurement module generates a potential difference signal via the measuring course; at least one pressure detector for measuring the pressure difference for solution flow from the inlet to the outlet of the annular flow channel to generate a pressure difference signal; and a calculation module, comprising calculating the zeta potential ξ_(m) at inside surface of the tube:

$\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$

where D is the permittivity, ζ_(ref) is the zeta potential of the reference cylinder, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model, the calculation module receives the potential difference signal and the pressure difference signal accompanying with the zeta potential ξ_(ref) of the reference cylinder which is known or measured in advance to calculate the zeta potential ξ_(m) at inside surface of the tube.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating the relative positions among the cylinder, reference tube, and annular flow channel according to a first embodiment of the present invention; and

FIG. 2 is a schematic diagram illustrating the measurement system for measuring the zeta potential of the cylinder's outer surface according to a second embodiment of the present invention.

FIG. 3 is a schematic diagram illustrating the relative positions among the tube, reference cylinder, and the annular flow channel according to a third embodiment of the present invention; and

FIG. 4 is a schematic diagram illustrating the measurement system for measuring the zeta potential at inside surface of the tube according to a fourth embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

What is probed into the invention is method and system for measuring the zeta potential of the cylinder's outer surface and the inside surface of the tube. Detail descriptions of the measuring procedures and system will be provided in the following in order to make the invention thoroughly understood. Obviously, the application of the invention is not confined to specific details familiar to those who are skilled in the art. On the other hand, the common process and procedures that are known to everyone are not described in details to avoid unnecessary limits of the invention. Some preferred embodiments of the present invention will now be described in greater detail in the following. However, it should be recognized that the present invention can be practiced in a wide range of other embodiments besides those explicitly described, that is, this invention can also be applied extensively to other embodiments, and the scope of the present invention is expressly not limited except as specified in the accompanying claims.

Referring to FIG. 1, a first embodiment of the present invention discloses a method for measuring the zeta potential of the cylinder's outer surface. At first, a cylinder 10 having a first radius R₁ and a reference tube 20 having a second radius R₂ are provided. The first radius R₁ is smaller than the second radius R₂. There is channel between the cylinder 10 and the reference tube 20 to form a annular flow channel 30. In addition, the cylinder 10 is coaxial with the reference tube 20. Next, a solution is introduced to the annular flow channel 30. After that, the solution is forced by a pressure difference ΔP to flow through the annular flow channel 30, wherein the flow direction of the solution is parallel to the axial direction of the reference tube 20. The net electric charges in the electric double layer on the two walls move along with the flow so as to generate streaming potential. A measuring process is performed to measure the streaming potential difference Ē between the two ends of the annular flow channel 30 by electrodes. Finally, the zeta potential ξ_(m) of the cylinder's outer surface is determined using the electrokinetic relationship as:

$\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$

where D is the permittivity [D=∈_(r)∈₀, where ∈_(r) is relative dielectric constant and ∈_(r) is dielectric constant in vacuum (=8.85×10⁻¹² C²J⁻¹m⁻¹)], ζ_(ref) is the zeta potential at the inner wall of the reference tube, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model.

In first embodiment, the cylinder 10 comprises one selected from the group consisting of the following: tubular membrane, capillary membrane, hollow fiber, fiber, and wire. In addition, if the cylinder is porous, the two ends of the cylinder are sealed to prevent the solution from flowing inside the cylinder to affect the measurement result. Moreover, the inner wall of the reference tube 20 is substantially smooth to prevent the solution from abnormal disturbance to affect the measurement result. Besides, the electric conductivity and the pH value of the solution can be measured in advance or by the measuring process.

In first embodiment, the correction factor F has a general expression as the following:

$F = {\frac{2}{\left( \frac{\zeta_{m}}{\zeta_{ref}} \right) + 1} + {\frac{1 - \frac{\zeta_{ref}}{\zeta_{m}}}{1 + \frac{\zeta_{ref}}{\zeta_{m}}} \times \frac{b^{2} - 1 - {2{b^{2} \cdot \ln}\; b}}{\ln \; {b \cdot \left( {1 - b^{2}} \right)}}} - {\frac{4 \cdot \left\lbrack {{I_{1}(\lambda)} - {b \cdot {I_{1}\left( {\lambda \; b} \right)}}} \right\rbrack}{\lambda \cdot \left( {1 - b^{2}} \right) \cdot \left( {1 + \frac{\zeta_{ref}}{\zeta_{m}}} \right)} \times \left\lbrack \frac{{K_{0}(\lambda)} - {\frac{\zeta_{ref}}{\zeta_{m}} \cdot {K_{0}\left( {\lambda \; b} \right)}}}{{{I_{0}\left( {\lambda \; b} \right)} \cdot {K_{0}(\lambda)}} - {{K_{0}\left( {\lambda \; b} \right)} \cdot {I_{0}(\lambda)}}} \right\rbrack} - {\frac{4 \cdot \left\lbrack {{b \cdot {K_{1}\left( {\lambda \; b} \right)}} - {K_{1}(\lambda)}} \right\rbrack}{\lambda \cdot \left( {1 - b^{2}} \right) \cdot \left( {1 + \frac{\zeta_{{ref}\;}}{\zeta_{m}}} \right)} \times \left\lbrack \frac{{\frac{\zeta_{ref}}{\zeta_{m}} \cdot {I_{0}\left( {\lambda \; b} \right)}} - {I_{0}(\lambda)}}{{{I_{0}\left( {\lambda \; b} \right)} \cdot {K_{0}(\lambda)}} - {{K_{0}\left( {\lambda \; b} \right)} \cdot {I_{0}(\lambda)}}} \right\rbrack}}$

where

${b = {R_{1}/R_{2}}},{\lambda = {R_{2}/\frac{1}{\kappa}}},$

κ (reciprocal Debye length) can be treated as the reciprocal of the thickness of the electric double layer, I₀ and I₁ are the zero-order and first order modified Bessel functions of first kind, respectively, and, K₀ and K₁ are the zero-order and first order modified Bessel functions of second kind, respectively.

Referring to FIG. 2, a second embodiment of the present invention discloses a measurement system for measuring the zeta potential of the cylinder's outer surface. The system comprises: a feeding module; a measurement module having a reference tube; a discharging module; at least one pressure detector; and a calculation module. The measurement module receives a solution from the feeding module, the solution is forced to flow through the inner side of the reference tube, which forms a straight flow channel, and then the solution is discharged to a discharging module so as to form a first measuring course. Thus, the measurement module generates a first potential difference signal via the first measuring course. Besides, the cylinder and the reference tube are assembled to form a second measuring course. The radius of the cylinder is smaller than that of the reference tube and the cylinder is coaxial with the reference tube. The solution received by the measurement module is forced to flow through the annular flow channel between the cylinder and the reference tube, and is discharged to the discharging module so as to form the second measuring course. The measurement module generates a second potential difference signal via the second measuring course.

The measurement module further comprises a first detector for measuring the streaming potential of the solution at the inlet of the flow channel, and a second detector for measuring the streaming potential of the solution at the outlet of the flow channel. In one case, the first detector and the second detector carry out detection in the first measuring course, so as to generate the first potential difference signal. In another case, the first detector and the second detector carry out detection in the second measuring course, so as to generate the second potential difference signal.

In second embodiment, the pressure detector is to measure the pressure difference between the two ends of the flow channel, so as to generate a pressure difference signal. Moreover, the calculation module comprises calculating the zeta potential ξ_(m) of the cylinder's outer surface:

$\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$

where D is the permittivity, ζ_(ref) is the zeta potential of the reference tube, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model (the general equation of F is described in the first embodiment). Additionally, the calculation module receives the first potential difference signal and the pressure difference signal to calculate the zeta potential of the inner surface of the reference tube. The calculation module receives the second potential difference signal and the pressure difference signal accompanying with the zeta potential of the inner surface of the reference tube to calculate the zeta potential of the outer surface of the cylinder. In addition, the measurement system further comprises an electric conductivity meter for measuring the electric conductivity of the solution and/or a pH meter for measuring the pH value of the solution.

In second embodiment, the cylinder comprises one selected from the group consisting of the following: tubular membrane, capillary membrane, hollow fiber, fiber, and wire. In addition, the two ends of the cylinders are sealed to prevent the solution from flowing inside the cylinder to affect the measurement result. Moreover, the inner wall of the reference tube is substantially smooth to prevent the solution from abnormal disturbance to affect the measurement result.

According to the foregoing description, the present invention discloses a method for measuring the zeta potential of the cylinder's outer surface. A cylinder having a first radius and a reference tube having a second radius are provided, wherein the first radius is smaller than the second radius. At first, the streaming potential due to solution flow in the single tube is used to obtain the zeta potential, ζ_(ref), at the inner wall of the reference tube. Then, the cylinder is placed coaxially inside the reference tube. After that, the solution is forced by a pressure difference ΔP to flow through the annular flow channel and then the streaming potential difference Ē between the two ends of the annular flow channel is measured by electrodes. Finally, the zeta potential ξ_(m) of the cylinder's outer surface is calculated by

$\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$

where D is the permittivity, ζ_(ref) is the zeta potential of the reference tube, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model. Furthermore, this invention also discloses a system for measuring the zeta potential of the cylinder's outer surface.

Referring to FIG. 3, a third embodiment of the present invention discloses a method for measuring the zeta potential at inside surface of the tube via the streaming potential in annular flow. At first, a tube 35 having a first radius R₁ and a reference cylinder 40 having a second radius R₂ are provided. The first radius R₁ is greater than the second radius R₂. There is a channel between the tube 35 and the reference cylinder 40 to form an annular flow channel 50. In addition, the tube 35 is coaxial with the reference 40. Next, a solution is introduced to the annular flow channel 50. After that, the solution is forced by a pressure difference ΔP to flow through the annular flow channel 50, wherein the flow direction of the solution is parallel to the axial direction of the reference cylinder 40. The net electric charges in the electric double layers on the two walls move along with the flow so as to generate streaming potential. A measuring process is performed to measure the streaming potential difference Ē between the two ends of the annular flow channel 50 by electrodes. Finally, the zeta potential ξ_(m) at inside surface of the tube is determined using the electrokinetic relationship as:

$\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k_{m}}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$

where D is the permittivity [D=∈_(r)∈₀, where ∈_(r) is relative dielectric constant and ∈_(r) is dielectric constant in vacuum (=8.85×10⁻¹² C²J⁻¹m⁻¹)], ζ_(ref) is the zeta potential of the reference cylinder, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model.

In third embodiment, the surface of the reference cylinder 40 is substantially smooth to prevent the solution from abnormal disturbance to affect the measurement result. Besides, the electric conductivity and the pH value of the solution can be measured in advance or by the measuring process.

In third embodiment, the correction factor F has a general expression as the following:

$F = {\frac{2}{\left( \frac{\zeta_{ref}}{\zeta_{m}} \right) + 1} + {\frac{1 - \frac{\zeta_{m}}{\zeta_{ref}}}{1 + \frac{\zeta_{m}}{\zeta_{ref}}} \times \frac{b^{2} - 1 - {2{b^{2} \cdot \ln}\; b}}{\ln \; {b \cdot \left( {1 - b^{2}} \right)}}} - {\frac{4 \cdot \left\lbrack {{I_{1}(\lambda)} - {b \cdot {I_{1}\left( {\lambda \; b} \right)}}} \right\rbrack}{\lambda \cdot \left( {1 - b^{2}} \right) \cdot \left( {1 + \frac{\zeta_{m}}{\zeta_{ref}}} \right)} \times \left\lbrack \frac{{K_{0}(\lambda)} - {\frac{\zeta_{m}}{\zeta_{ref}} \cdot {K_{0}\left( {\lambda \; b} \right)}}}{{{I_{0}\left( {\lambda \; b} \right)} \cdot {K_{0}(\lambda)}} - {{K_{0}\left( {\lambda \; b} \right)} \cdot {I_{0}(\lambda)}}} \right\rbrack} - {\frac{4 \cdot \left\lbrack {{b \cdot {K_{1}\left( {\lambda \; b} \right)}} - {K_{1}(\lambda)}} \right\rbrack}{\lambda \cdot \left( {1 - b^{2}} \right) \cdot \left( {1 + \frac{\zeta_{m}}{\zeta_{ref}}} \right)} \times \left\lbrack \frac{{\frac{\zeta_{m}}{\zeta_{ref}} \cdot {I_{0}\left( {\lambda \; b} \right)}} - {I_{0}(\lambda)}}{{{I_{0}\left( {\lambda \; b} \right)} \cdot {K_{0}(\lambda)}} - {{K_{0}\left( {\lambda \; b} \right)} \cdot {I_{0}(\lambda)}}} \right\rbrack}}$

where

${b = {R_{1}/R_{2}}},{\lambda = {R_{2}/\frac{1}{\kappa}}},$

κ (reciprocal Debye length) can be treated as the reciprocal of the thickness of the electric double layer, I₀ and I₁ are the zero-order and first order modified Bessel functions of first kind, respectively, and, K₀ and K₁ are the zero-order and first order modified Bessel functions of second kind, respectively.

Referring to FIG. 4, a fourth embodiment of the present invention discloses a measurement system for measuring the zeta potential at inside surface of the tube via the streaming potential in annular flow. The system comprises: a feeding module; a measurement module; at least one pressure detector; and a calculation module. The measurement module comprises a tube and a reference cylinder, wherein the radius of the tube is greater than the radius of reference cylinder. The zeta potential of reference cylinder is known or measured in advance, and the reference cylinder is held coaxially inside the tube. The measurement module receives a solution from the feeding module, the solution is forced to flow through an annular flow channel between the reference cylinder and the tube, and then the solution is discharged to a discharging module so as to form a measuring course, and thus the measurement module generates a potential difference signal via the measuring course.

The measurement module further comprises a first detector for measuring the streaming potential at the inlet of the flow channel, and a second detector for measuring the streaming potential at the outlet of the flow channel. In one case, the first detector and the second detector carry out detection in the measuring course, so as to generate the potential difference signal.

In fourth embodiment, the pressure detector is to measure the pressure difference between the two ends of the flow channel, so as to generate a pressure difference signal. Moreover, the calculation module comprises calculating the zeta potential ξ_(m) at surface of the tube:

$\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k_{m}}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$

where D is the permittivity, ζ_(ref) is the zeta potential of the reference cylinder, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model (the general equation of F is described in the first embodiment). Additionally, the calculation module receives the potential difference signal and the pressure difference signal to calculate the zeta potential at surface of the tube. In addition, the measurement system further comprises an electric conductivity meter for measuring the electric conductivity of the solution and/or a pH meter for measuring the pH value of the solution.

In fourth embodiment, the reference cylinder is a solid object or the two ends of the reference cylinders are sealed, so as to prevent the solution from flowing inside the reference cylinder to affect the measurement result. Moreover, the surface of the reference cylinder is substantially smooth to prevent the solution from abnormal disturbance to affect the measurement result.

According to the foregoing description, the present invention discloses another method for measuring the zeta potential at inside surface of the tube. A tube having a first radius and a reference cylinder having a second radius are provided, wherein the first radius is greater than the second radius.

The reference cylinder is held coaxially inside the tube, and the channel existing between the tube and the reference cylinder forms an annular flow channel. After that, the solution is forced by a pressure difference ΔP to flow through the annular flow channel and then the streaming potential difference Ē between the two ends of the annular flow channel is measured by electrodes. Finally, the zeta potential ξ_(m) at inside surface of the tube is calculated by:

$\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k_{m}}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$

where D is the permittivity, ζ_(ref) is the zeta potential of the reference cylinder, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model.

Obviously many modifications and variations are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims the present invention can be practiced otherwise than as specifically described herein. Although specific embodiments have been illustrated and described herein, it is obvious to those skilled in the art that many modifications of the present invention may be made without departing from what is intended to be limited solely by the appended claims. 

1. A method for measuring the zeta potential at inside surface of the tube, comprising: providing a tube having a first radius and a reference cylinder having a second radius, wherein the first radius is greater than the second radius, and the reference cylinder is held coaxially inside the tube, and the channel existing between the tube and the reference cylinder forms an annular flow channel; introducing a solution to the annular flow channel, and the solution is forced by a pressure difference ΔP to flow through the annular flow channel, wherein the flow direction of the solution is parallel to the axial direction of the reference cylinder; performing a measuring process to measure the streaming potential difference Ē between the two ends of the annular flow channel by electrodes, wherein the measuring process comprises calculating the zeta potential ξ_(m) at inside surface of the tube from the following equation: $\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k_{m}}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$ where D is the permittivity, ζ_(ref) is the zeta potential of the reference cylinder, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model.
 2. The method according to claim 1, wherein the radius of the tube is at greater than millimeter scale.
 3. The method according to claim 1, wherein the surface of the reference cylinder is substantially smooth.
 4. The method according to claim 1, wherein the measuring process further comprises measuring the electric conductivity k of the solution.
 5. The method according to claim 1, wherein the measuring process further comprises measuring the pH value of the solution.
 6. The method according to claim 1, wherein the correction factor F has a general expression as the following: $F = {\frac{2}{\left( \frac{\zeta_{ref}}{\zeta_{m}} \right) + 1} + {\frac{1 - \frac{\zeta_{m}}{\zeta_{ref}}}{1 + \frac{\zeta_{m}}{\zeta_{ref}}} \times \frac{b^{2} - 1 - {2{b^{2} \cdot \ln}\; b}}{\ln \; {b \cdot \left( {1 - b^{2}} \right)}}} - {\frac{4 \cdot \left\lbrack {{I_{1}(\lambda)} - {b \cdot {I_{1}\left( {\lambda \; b} \right)}}} \right\rbrack}{\lambda \cdot \left( {1 - b^{2}} \right) \cdot \left( {1 + \frac{\zeta_{m}}{\zeta_{ref}}} \right)} \times \left\lbrack \frac{{K_{0}(\lambda)} - {\frac{\zeta_{m}}{\zeta_{ref}} \cdot {K_{0}\left( {\lambda \; b} \right)}}}{{{I_{0}\left( {\lambda \; b} \right)} \cdot {K_{0}(\lambda)}} - {{K_{0}\left( {\lambda \; b} \right)} \cdot {I_{0}(\lambda)}}} \right\rbrack} - {\frac{4 \cdot \left\lbrack {{b \cdot {K_{1}\left( {\lambda \; b} \right)}} - {K_{1}(\lambda)}} \right\rbrack}{\lambda \cdot \left( {1 - b^{2}} \right) \cdot \left( {1 + \frac{\zeta_{m}}{\zeta_{ref}}} \right)} \times \left\lbrack \frac{{\frac{\zeta_{m}}{\zeta_{ref}} \cdot {I_{0}\left( {\lambda \; b} \right)}} - {I_{0}(\lambda)}}{{{I_{0}\left( {\lambda \; b} \right)} \cdot \; {K_{0}(\lambda)}} - {{K_{0}\left( {\lambda \; b} \right)} \cdot {I_{0}(\lambda)}}} \right\rbrack}}$ Where ${b = {R_{1}/R_{2}}},{\lambda = {R_{2}/\frac{1}{\kappa}}},$ κ (reciprocal Debye length) can be treated as the reciprocal of the thickness of the electric double layer, I₀ and I₁ are the zero-order and first order modified Bessel functions of first kind, respectively, and, K₀ and K₁ are the zero-order and first order modified Bessel functions of second kind, respectively.
 7. A system for measuring the zeta potential at inside surface of the tube, comprising: a feeding module; a measurement module comprising a reference cylinder and a tube, wherein the reference cylinder is held coaxially inside the tube, and the radius of the tube is greater than the radius of reference cylinder, and the zeta potential of reference cylinder is known or measured in advance, wherein the measurement module receives a solution from the feeding module, the solution is forced to flow through an annular flow channel between the reference cylinder and the tube, and then the solution is discharged to a discharging module so as to form a measuring course, and thus the measurement module generates a potential difference signal via the measuring course; at least one pressure detector for measuring the pressure difference for solution flow from the inlet to the outlet of the annular flow channel to generate a pressure difference signal; and a calculation module, comprising calculating the zeta potential ξ_(m) at inside surface of the tube: $\frac{\overset{\_}{E}}{\Delta \; P}=={{- \frac{D}{\mu \; k}}\left( \frac{\zeta_{m} + \zeta_{ref}}{2} \right)F}$ where D is the permittivity, ζ_(ref) is the zeta potential of the reference cylinder, μ is the viscosity of the solution, k is the electric conductivity of the solution, and F is a correction factor for the electrokinetic model, the calculation module receives the potential difference signal and the pressure difference signal accompanying with the zeta potential ξ_(ref) of the reference cylinder which is known or measured in advance to calculate the zeta potential ξ_(m) at inside surface of the tube.
 8. The method according to claim 7, wherein the radius of the tube is at greater than millimeter scale.
 9. The system according to claim 7, wherein the surface of the reference cylinder is substantially smooth.
 10. The system according to claim 7, wherein the reference cylinder is a solid object or the two ends of the reference cylinders are sealed, so as to prevent the solution from flowing through the reference cylinder to affect the measurement result.
 11. The system according to claim 7, wherein the measurement module further comprises a first detector for measuring the streaming potential at the inlet of the flow channel, and a second detector for measuring the streaming potential at the outlet of the flow channel, so as to generate the potential difference signal.
 12. The system according to claim 7, wherein the correction factor F has a general equation as the following: $F = {\frac{2}{\left( \frac{\zeta_{ref}}{\zeta_{m}} \right) + 1} + {\frac{1 - \frac{\zeta_{m}}{\zeta_{ref}}}{1 + \frac{\zeta_{m}}{\zeta_{ref}}} \times \frac{b^{2} - 1 - {2{b^{2} \cdot \ln}\; b}}{\ln \; {b \cdot \left( {1 - b^{2}} \right)}}} - {\frac{4 \cdot \left\lbrack {{I_{1}(\lambda)} - {b \cdot {I_{1}\left( {\lambda \; b} \right)}}} \right\rbrack}{\lambda \cdot \left( {1 - b^{2}} \right) \cdot \left( {1 + \frac{\zeta_{m}}{\zeta_{ref}}} \right)} \times \left\lbrack \frac{{K_{0}(\lambda)} - {\frac{\zeta_{m}}{\zeta_{ref}} \cdot {K_{0}\left( {\lambda \; b} \right)}}}{{{I_{0}\left( {\lambda \; b} \right)} \cdot {K_{0}(\lambda)}} - {{K_{0}\left( {\lambda \; b} \right)} \cdot {I_{0}(\lambda)}}} \right\rbrack} - {\frac{4 \cdot \left\lbrack {{b \cdot {K_{1}\left( {\lambda \; b} \right)}} - {K_{1}(\lambda)}} \right\rbrack}{\lambda \cdot \left( {1 - b^{2}} \right) \cdot \left( {1 + \frac{\zeta_{m}}{\zeta_{ref}}} \right)} \times \left\lbrack \frac{{\frac{\zeta_{m}}{\zeta_{ref}} \cdot {I_{0}\left( {\lambda \; b} \right)}} - {I_{0}(\lambda)}}{{{I_{0}\left( {\lambda \; b} \right)} \cdot {K_{0}(\lambda)}} - {{K_{0}\left( {\lambda \; b} \right)} \cdot {I_{0}(\lambda)}}} \right\rbrack}}$ Where ${b = {R_{1}/R_{2}}},{\lambda = {R_{2}/\frac{1}{\kappa}}},$ κ (reciprocal Debye length) can be treated as the reciprocal of the thickness of the electric double layer, I₀ and I₁ are the zero-order and first order modified Bessel functions of first kind, respectively, and, K₀ and K₁ are the zero-order and first order modified Bessel functions of second kind, respectively. 